Weak Perspective Camera Model Research Articles

Computing Smooth Time Trajectories for Camera and Deformable Shape in Structure from Motion with Occlusion

We address the classical computer vision problems of rigid and nonrigid structure from motion (SFM) with occlusion. We assume that the columns of the input observation matrix W describe smooth 2D point trajectories over time. We then derive a family of efficient methods that estimate the column space of W using compact parameterizations in the Discrete Cosine Transform (DCT) domain. Our methods tolerate high percentages of missing data and incorporate new models for the smooth time trajectories of 2D-points, affine and weak-perspective cameras, and 3D deformable shape. We solve a rigid SFM problem by estimating the smooth time trajectory of a single camera moving around the structure of interest. By considering a weak-perspective camera model from the outset, we directly compute euclidean 3D shape reconstructions without requiring postprocessing steps such as euclidean upgrade and bundle adjustment. Our results on real SFM data sets with high percentages of missing data compared positively to those in the literature. In nonrigid SFM, we propose a novel 3D shape trajectory approach that solves for the deformable structure as the smooth time trajectory of a single point in a linear shape space. A key result shows that, compared to state-of-the-art algorithms, our nonrigid SFM method can better model complex articulated deformation with higher frequency DCT components while still maintaining the low-rank factorization constraint. Finally, we also offer an approach for nonrigid SFM when W is presented with missing data.

Robust stabilization of second-order image-based affine systems

In this paper, the problem of robust relative positioning between a 6-DOF robot camera and an object of interest is considered. Assuming weak perspective camera model and local linear approximation of visible object's surface, an image-based state space representation of robot camera–object interaction model is derived, based on the matrix of 2-D affine transformations. Dynamic extension of the visual model permits to estimate 3-D parameters directly as functions of state variables. The proposed nonlinear robust control law ensures asymptotic stability but at image singularities, assuming exact model and state measurements. In the presence of bounded uncertainties, under appropriate choice of control gains, ultimate boundedness of the state error is also formally proved. Simulation results validate the theoretical framework both in terms of system convergence and control robustness.

Pose Estimation using Point and Line Correspondences

The problem of a real-time pose estimation between a 3D scene and a single camera is a fundamental task in most 3D computer vision and robotics applications such as object tracking, visual servoing, and virtual reality. In this paper we present two fast methods for estimating the 3D pose using 2D to 3D point and line correspondences. The first method is based on the iterative use of a weak perspective camera model and forms a generalization of DeMenthon's method (1995) which consists of determining the pose from point correspondences. In this method the pose is iteratively improved with a weak perspective camera model and at convergence the computed pose corresponds to the perspective camera model. The second method is based on the iterative use of a paraperspective camera model which is a first order approximation of perspective. We describe in detail these two methods for both non-planar and planar objects. Experiments involving synthetic data as well as real range data indicate the feasibility and robustness of these two methods. We analyse the convergence of these methods and we conclude that the iterative paraperspective method has better convergence properties than the iterative weak perspective method. We also introduce a non-linear optimization method for solving the pose problem.

Object Pose: The Link between Weak Perspective,Paraperspective, and Full Perspective

Recently, DeMenthon and Davis (1992, 1995) proposed a method for determining the pose of a 3-D object with respect to a camera from 3-D to 2-D point correspondences. The method consists of iteratively improving the pose computed with a weak perspective camera model to converge, at the limit, to a pose estimation computed with a perspective camera model. In this paper we give an algebraic derivation of DeMenthon and Davis‘ method and we show that it belongs to a larger class of methods where the perspective camera model is approximated either at zero order (weak perspective) or first order (paraperspective). We describe in detail an iterative paraperspective pose computation method for both non coplanar and coplanar object points. We analyse the convergence of these methods and we conclude that the iterative paraperspective method (proposed in this paper) has better convergence properties than the iterative weak perspective method. We introduce a simple way of taking into account the orthogonality constraint associated with the rotation matrix. We analyse the sensitivity to camera calibration errors and we define the optimal experimental setup with respect to imprecise camera calibration. We compare the results obtained with this method and with a non-linear optimization method.